Industrial Mathematics - Alexiades
           
                    Project 1:
      Ostwald ripening model - Fate of single-size crystals
The objective of this Project is to verify numerically the theoretical predictions 
for the Ostwald ripening model with single-size crystals.
See guidelines in Guide for preparing reports. 

The parameter values are as in Lab 4 (and g=d=1):
	μ=1.e-3,  c*=7.52e-7,  γ=4.e-3,  c0=1.05c*,  k=5.e7

In the Introduction, describe (briefly) the physical problem.
Under Problem Statement,  state fully the mathematical 
problem that models the physical problem 
(physical assumptions, ODE, initial condition, parameter values).
Under Methods, say a few words about Newton-Raphson and Euler scheme.

Then, for each of the cases below, do the following:

 a. Discuss the equilibria, and what fate the theory predicts.
 b. Compute the time-evolution of the size (numerically by necessity). 
 c. Plot it (choosing the scale wisely) and annotate the plot (by hand would be ok).
 d. Discuss the behavior of the numerical solution, relevance to the theory, and physical implications.

Cases:
1. For x* = 0.05,   find x(t) up to time tend = 0.1 .

2. For x* = 0.0975, find x(t) up to time tend = 0.1 .

3. For x* = 0.08 and mu = 1.d-5, find x(t) up to time of dissolution.  
   For this case, your code should be checking if xn ≈ 0.0 at each time-step, 
   and if so it should do what is needed and exit.  
   Trouble is, this will find the dissolution time only to within Δt.  
   How could you find it more accurately ???

The report for the project should be turned in on paper, typeset or handwritten 
(whichever you find more convenient, but nice and neat).

The important aspect here is the presentation, as if "to your boss"
(who is not necessarity an expert in the subject)... see the guidelines...